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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdinex2 | GIF version |
Description: Bounded version of inex2 3913. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdinex2.bd | ⊢ BOUNDED 𝐵 |
bdinex2.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
bdinex2 | ⊢ (𝐵 ∩ 𝐴) ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3158 | . 2 ⊢ (𝐵 ∩ 𝐴) = (𝐴 ∩ 𝐵) | |
2 | bdinex2.bd | . . 3 ⊢ BOUNDED 𝐵 | |
3 | bdinex2.1 | . . 3 ⊢ 𝐴 ∈ V | |
4 | 2, 3 | bdinex1 10690 | . 2 ⊢ (𝐴 ∩ 𝐵) ∈ V |
5 | 1, 4 | eqeltri 2151 | 1 ⊢ (𝐵 ∩ 𝐴) ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 Vcvv 2601 ∩ cin 2972 BOUNDED wbdc 10631 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-bdsep 10675 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 df-bdc 10632 |
This theorem is referenced by: bdssex 10693 |
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